Flute hole calculator
Choose the flute's lowest note (all holes closed), the hole pattern and the tube. The calculator gives the length and the position of every hole, from the embouchure and from the end, with the corrections for the open end, the embouchure and each hole's chimney.
D flute in 20 mm PVC (estimate)
Transverse flute in D4 (293.7 Hz), 20 mm solvent-weld PVC (17 mm inside, 1.5 mm wall), 9 mm embouchure, 9.5 mm holes, at 25 °C, A 440 Hz.
| Hole | Note | Diameter (mm) | From embouchure (mm) | From end (mm) |
|---|---|---|---|---|
| 1 | E4 | 9.5 | 477.8 | 79.5 |
| 2 | F♯4 | 9.5 | 420.8 | 136.5 |
| 3 | G4 | 9.5 | 399.1 | 158.2 |
| 4 | A4 | 9.5 | 347.0 | 210.3 |
| 5 | B4 | 9.5 | 305.2 | 252.1 |
| 6 | C♯5 | 9.5 | 267.6 | 289.7 |
How to use it
- Choose the type, the fundamental note and the hole pattern (6 holes gives a major scale, like a fife or tin whistle).
- Tap a ready-made tube or enter your tube's inside diameter, wall and embouchure. The fields are in millimeters (1″ = 25.4 mm).
- Change each hole's diameter right in the table: positions update instantly, and warnings flag overlapping holes or holes too far apart for your fingers.
Help and explanations
A D flute (293.7 Hz) in 20 mm PVC, with a 9 mm embouchure and 9.5 mm (3/8″) holes, comes out 557.3 mm (21.94″) from embouchure to end. It's an estimate: always tune on the real tube.
How it's calculated
The calculator follows Pete Kosel's Flutomat, which applies Arthur Benade's equations. A tube open at both ends sounds a half wavelength, L = c ÷ 2f, with c = 331.3 · √(1 + T ÷ 273.15), 346.1 m/s at 25 °C (77 °F). Three corrections follow from there: the open end, the embouchure and each hole's chimney, which depends on the wall thickness and the hole diameter. That's why a smaller hole sits closer to the embouchure.
Transverse, end-blown and ring flutes
The transverse flute is the most accurate case. On the quena, shakuhachi and ney the air strikes an edge, and on the suling it passes through a ring: those types are estimates. Cut about 5/8″ (15 mm) long and tune by shortening.
US PVC sizes
In the US, 1/2″ Schedule 40 PVC has a 0.622″ (15.8 mm) inside diameter and a 0.109″ (2.77 mm) wall: enter those numbers. A D flute on it, with the same 9 mm embouchure and 9.5 mm holes, comes out 544.0 mm (21.42″) from embouchure to end.
From calculation to a tuned flute
Drill about 2 mm (5/64″) smaller than shown, play, check with a tuner and open the hole up gradually with a round file: a bigger hole raises the pitch. Start with the bottom hole, because every open hole shifts the ones above it.
Tips
- Tune hole by hole with the Lalatone tuner, blowing gently: overblowing sharpens the note.
- On bamboo, use the average inside diameter of the two ends and clear out the internal nodes.
- For a pipe closed at the bottom, like a pan flute, use the wind chime and pan flute calculator.
Frequently asked questions
What are the measurements for a D PVC flute?
20 mm PVC (17 mm inside), 9 mm embouchure, 9.5 mm holes, at 25 °C: 557.3 mm (21.94″) from embouchure to end, with holes at 79.5, 136.5, 158.2, 210.3, 252.1 and 289.7 mm from the end.
Where does the cork go on a transverse flute?
1 to 1.5 times the embouchure diameter above its center: with a 9 mm embouchure, 9 to 13.5 mm.
Does hole size change the hole position?
Yes. In the D example, a 7 mm first hole sits 6.7 mm closer to the embouchure than a 9.5 mm one.
How big should the embouchure hole be?
On a 17 mm bore, 9 to 10 mm. Too big and the tone turns breathy.
Does it work for a quena or a bamboo flute?
For a transverse bamboo flute, yes. For quena, shakuhachi and ney it's an estimate: the same D tube comes out at 576.4 mm.
What if the holes are too far apart for my fingers?
On the D PVC flute, holes 1 and 2 are 57 mm (2.24″) apart. Use a smaller bottom hole, which moves up the tube, or offset the hole to one side.